Problem: What is the greatest common factor of $6a$, $8a^{2}$, and $14$ ?
Answer: Let's factor each monomial to its prime factors: $\begin{aligned} 6a&=(2)(3)(a) \\\\ 8a^{2}&=(2)(2)(2)(a)(a) \\\\ 14&=(2)(7) \end{aligned}$ We want the largest set of factors that's included in all three monomials. All of the monomials have one factor of $ 2$. $\begin{aligned} 6a&=( 2)(3)(a) \\\\ 8a^{2}&=( 2)(2)(2)(a)(a) \\\\ 14&=( 2)(7) \end{aligned}$ This is the greatest common factor: $ 2$